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Empirical likelihood confidence regions of the parameters in a partially linear single-index model

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Science china Mathematics 2005年第10期48卷 1333-1348页

作者： XUE Liugen~1 & ZHU Lixing~2.1. College of applied sciences,{2. university of technology,{2. 10002.,china 2. Department of Mathematics,Hong Kong Baptist university,Hong Kong,china 1. College of applied sciences Beijing University of Technology 100022 Beijing China 2. Department of Mathematics Hong Kong Baptist University Hong Kong China

In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.

关键词： partially linear single-index model, empirical likelihood, confidence region, chi-square distribution, coverage probability.

On some tests-based projection pursuit for elliptical symmetry of a high-dimensional distribution

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Chinese Science Bulletin 1998年第6期43卷 450-458页

作者： JING Ping 1 and ZHU Lixing 2.1. Mathematics Lab, china university of Mining & {2., beijing 100083, china 2. Probability Lab, Institute of applied Mathematics, Chinese Academy of sciences, beijing 100080, china Mathematics Lab China University of Mining & Technology Beijing China Probability Lab Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.

关键词： bootstrap approximation projection pursuit type statistic elliptical symmetry.

A new DNA algorithm to solve graph coloring problem

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Progress in Natural Science:Materials International 2007年第6期17卷 733-738页

作者： Jiang Xingpeng1, Li Yin2. Meng Ya3 and Meng Dazhi2.1. National Laboratory of Pattern Recognition,Institute of Automation, Chinese Academy of sciences, beijing 100080,{2. 2. College of applied sciences, beijing university of technology, beijing 10002.,{2. 3. School of Science, beijing Institute of technology, beijing 100081,{2.) National Laboratory of Pattern Recognition Institute of Automation Chinese Academy of Sciences Beijing 100080 China College of applied sciences Beijing University of Technology Beijing 100022 China School of Science Beijing Institute of Technology Beijing 100081 China

Using a small quantity of DNA molecules and little experimental time to solve complex problems successfully is a goal of DNA computing. Some NP-hard problems have been solved by DNA computing with lower time complexity than conventional computing. However, this advantage often brings higher space complexity and needs a large number of DNA encoding molecules. One example is graph coloring problem. Current DNA algorithms need exponentially increasing DNA encoding strands with the growing of problem size. Here we propose a new DNA algorithm of graph coloring problem based on the proof of four-color theorem. This algorithm has good properties of needing a relatively small number of operations in polynomial time and needing a small number of DNA encoding molecules (we need only 6R DNA encoding molecules if the number of regions in a graph is R).

关键词： DNA computing NP-hard problem graph coloring problem.

Existence of solutions for the dynamic equation of ferrimagnets

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Progress in Natural Science:Materials International 2007年第11期17卷 1279-1283页

作者： Zeng Ming1, Guo Boling2.and Cheng Caozong1(1. College of applied sciences,{2., beijing 10002., china 2. Center for Nonlinear Studies, Institute of applied Physics and Computational Mathematics, beijing 100088, china) College of applied sciences Beijing University of Technology Beijing 100022 China Center for Nonlinear Studies Institute of Applied Physics and Computational Mathematics Beijing 100088 China

Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.

关键词： ferrimagnet weak solutions penalized method finite difference method

Explanation of the mechanism of carcinogenesis and syntheses of anticancer agents with high selectivity

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Science china Chemistry 2006年第1期49卷 44-62页

作者： DAI Qianhuan1,2.1. Center of Chemistry and Bioengineering of Cancer Research, beijing Polytechnic university (Now known as beijing Univer-sity of technology), beijing 10002., china 2. Center of Environmental sciences, Peking university, beijing 100871, china 1. Center of Chemistry and Bioengineering of Cancer Research Beijing Polytechnic University Beijing 100022 China 2. Center of Environmental sciences Peking University Beijing 100871 China

In 1979, the mechanism of chemical carcinogenesis, a challenging anddifficult scientific problem pending for a number of years, was explained by Dai Qianhuan. Themechanism named di-region theory predicted that a carcinogen always metabolizes to form a specialbi-functional alky-lating agent. This agent induces cross-linkages between the complementary basepairs in DMA and switches on initial mutageneses in genomes including point and frameshiftmutations. This, in turn, induces further deep mutageneses including the production of variouschimeric chromosomes, deletions and other aberrations found in genomes. In the end this initiatescarcinogenesis of the whole cell through the reverse transcription mechanism after a lengthyincubation period. Recently, this laboratory has verified that physical carcinogenesis, includingthe oncogenesis induced by radiation and asbestos as well as the carcinogenesis induced byendogenous factors such as estrogen or diethyl-stilbestrol switch on carcinogenesis by inducing theformation of cross-linkages between the complementary base pairs in DNA. Di-region theory has nowbeen supported by many experimental observations such as mutational spectra of various *** potential for carcinogenesis, teratogenesis, sterility and mutagenesis lumped together asgenetic toxicity appears to originate almost uniformly from the cross-linking between complementarybases, i.e. malignant cross-linking, which is in accordance with di-region theory. Other forms ofcross-linking between non-complementary bases, benign cross-linkings, show bi-functional alkylationanticancer activity but lack genetic toxicity. The predictable design and synthesis of a highselectivity anticancer agent with high efficacy and low genetic toxicity, a goal long pursued incancer chemotherapy, have been realized for the first time in this laboratory by inhibitingmalignant and heightening benign cross-linking using the principles of di-region theory. A series ofpatented new anticanc

关键词： mechanism of carcinogenesis, di-region theory, minoplatin, selectivity of anticancer agent, cross-linking between DNA bases, anticancer platinum complexes, predictive design of anticancer agent, second generation anticancer agent.

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2.1. Department of Mathematics, beijing Normal university, beijing 100875, china 2. Institute of applied Physics and Computational Mathematics, beijing 100080, china 1. Department of Mathematics Beijing Normal University Beijing 100875 China 2. Institute of applied Physics and Computational Mathematics Beijing 100080 China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

On three-dimensional geological modeling and visualization

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Science china Earth sciences 2004年第8期47卷 739-748页

作者： WU Qiang1 & XU Hua2.1. Department of Resource Exploitation Engineering, china university of Mining and {2., beijing 100083, china 2. beijing Institute of Petrochemical {2., beijing 102.17, china 1. Department of Resource Exploitation Engineering China University of Mining and Technology 100083 Beijing China 2. beijing Institute of Petrochemical technology 102617 Beijing China

The technology of 3D geological modeling will bring about great changes in the methods of geological data acquiring, storing, processing and displaying. However, no perfect or convenient software systems have been developed up to now since the geologic data which re-flect geological entities bear the feature of diversity, uncertainty and complexity. Some supervoxel models, mathematical models of fault and geometrical models of fold have been contrived so as to show the space geometric configuration of the complicated geologic structures. The application-oriented system architecture for 3D geological modeling is established; and a novel design concept based on spatial data processing is also proposed with the technology of solid modeling as its core and the application of models as its objective. Theories and methods for 3D geological modeling will hopefully be enriched and developed. In the light of these theories and methods, a feature-based navigation visualization technique is also put forward in the paper. By integrating geo-database, graphics libraries and KBS with 3D dynamic simulation systems, geologists will be able to capture the partial characteristics and whole structure embodied in the geological data in a direct-viewing, figurative and accurate manner.

关键词： 3D geological modeling,geometrical model,system architecture,visualization

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Science china Earth sciences 2004年第10期47卷 896-911页

作者： ZHANG Changhou1,2. WU Ganguo1,2. WANG Genhou2. ZHANG Weijie2.& SONG Honglin2.1. Key Laboratory of Lithospheric Tectonics and Lithoprobing technology, china {2. of Geosciences, Ministry of Education of china, beijing 100083, china 2. School of Earth sciences and Mineral Resources, china {2. of Geosciences, beijing 100083, china 1. Key Laboratory of Lithospheric Tectonics and Lithoprobing technology China University of Geosciences Ministry of Education of China 100083 Beijing China 2. School of Earth sciences and Mineral Resources China University of Geosciences 100083 Beijing China

The northwest trending tectonic belt in the middle part of the Mesozoic intraplate Yanshan Orogenic Belt, northeast Hebei Province, is composed of thrusts, extensional faults, strike-slip faults and syntectonic sedimentations as well. The northeastward basement-involved major thrusting deformation occurred between 174Ma and 168MaBP and was followed by an intrusion of the granitic plutonic rocks. As a part of the post-thrusting extensional deformations a northwest extending volcano-sedimentation system of Late Jurassic and Early Cretaceous formed in the southwest side of the belt. These volcano-sedimentary sequences are divided into Tuchengzi Formation, Zhangjiakou Formation, Yixian Formation and Jiufotang Formation re- spectively. They are characterized by southeastward migration as a result of the increasing down-dip slip displacement along the major extensional fault toward the southeast of the belt. The provenance area of the Jiufotang Formation north to it experienced southwestward thrusting during and after its later sedimentation. The thrusting in this stage resulted in the formation of an asymmetric footwall syncline with vergence to SW in the Jiufotang Formation in the NE side of the basin. Finally a dextral strike-slip deformation occurred along the NW tectonic belt. The striking tectono-geomorphological features and present seismic activities along this belt indicate that it has been being active since Cenozoic era and is still in the active state at present. This northwest extending tectonic belt was following the same direction and location as the existing fault systems within the basement as revealed by former geological and geophysical studies. So it is reasonable to infer the Mesozoic deformation along this belt to be a result of reactivation of the basement structures in a favorable tectonic stress field. The reactivation of basement struc- tures might be taken as one of the mechanisms of intraplate deformation and orogeny.

关键词： Yanshan Orogenic Belt, northwest extending tectonic complex, thrust system, geochronology.

Simultaneous variable selection for heteroscedastic regression models

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Science china Mathematics 2011年第3期54卷 515-530页

作者： ZHANG ZhongZhan1 & WANG DaRong2.1College of applied sciences,{2., beijing 10012., china 2.he Pilot College,{2., beijing 101101, china 1. College of applied sciences Beijing University of Technology Beijing 100124 China2. The Pilot College Beijing University of Technology Beijing 101101 China

In this paper, we propose a new criterion, named PICa, to simultaneously select explanatory variables in the mean model and variance model in heteroscedastic linear models based on the model structure. We show that the new criterion can select the true mean model and a correct variance model with probability tending to 1 under mild conditions. Simulation studies and a real example are presented to evaluate the new criterion, and it turns out that the proposed approach performs well.

关键词： variable selection heteroscedastic regression models adjusted profile log-likelihood AIC BIC